Approximate likelihood and pseudo‐likelihood inference in meta‐analysis of diagnostic accuracy studies accounting for disease prevalence and study design

Bivariate random‐effects models represent a recommended approach for meta‐analysis of diagnostic test accuracy, jointly modeling study‐specific sensitivity and specificity. As the severity of the disease status can vary across studies, a proper analysis should account for the dependence of the accuracy measures on the disease prevalence. To this aim, trivariate generalized linear mixed‐effects models have been proposed in the literature, although computational difficulties strongly limit their applicability. In addition, the attention has been mainly paid to cohort studies, where the study‐specific disease prevalence can be estimated from, while information from case‐control studies is often neglected. To overcome such limits, this article introduces a trivariate approximate normal model, which accounts for disease prevalence along with accuracy measures in cohort studies and sensitivity and specificity in case‐control studies. The model represents an extension of the bivariate normal mixed‐effects model originally developed for meta‐analysis not accounting for disease prevalence, under an approximate normal within‐study distribution for the logit of estimated sensitivity and specificity. The components of the approximate within‐study covariance matrix are derived and the likelihood function is obtained in closed‐form. The approximate likelihood approach is compared to that based on the exact within‐study distribution and to its modifications following a pseudo‐likelihood strategy aimed at reducing the computational effort. The comparison is based on simulation studies in a variety of scenarios, and illustrated in a meta‐analysis about the accuracy of a test to diagnose fungal infection and a meta‐analysis of a noninvasive test to detect colorectal cancer.